Answer:
A
Step-by-step explanation:
To complete this problem, we can use the rules of PEMDAS to simplify the problem.
PEMDAS is an acronym used to calculate an expression based on the order of operations it must be done in.
[tex]PEMDAS~stands~for: \begin{cases} P & \text{Parenthesis} \\ E & \text{Exponent} \\ M & \text{Multiplication} \\ D & \text{Division} \\ A & \text{Addition} \\ S & \text{Subtraction}\end{cases}[/tex]
Based on the initial expression [tex]\frac{7}{2}h-3(5h-\frac{1}{2})[/tex], we must first work on distributing the parenthesis so we can start combining like terms.
[tex]\frac{7}{2}h-3(5h-\frac{1}{2})[/tex]
- Distribute the [tex]-3[/tex] to [tex]5h[/tex] and [tex]-\frac{1}{2}[/tex].
[tex]\frac{7}{2}h-15h+\frac{3}{2}[/tex]
- Now that there is no parenthesis, we can start combining like terms by converting [tex]15h[/tex] to [tex]\frac{30}{2}h[/tex] to have the same denominator.
[tex]\frac{7}{2}h-\frac{30}{2}h+\frac{3}{2}[/tex]
[tex]\frac{-23}{2} h+\frac{3}{2}[/tex]
Thus, our expression is equal to choice A.
